However a closer fit is achieved with 77 as the multiplier.
That’s because 68/77 = 0.8831168, almost identical to the decimal place values above.
(Incidentally 68 = 34 x 2 which are both Fibonacci numbers).
An expanded model with 77 times the values of the original, has whole numbers of orbits:
1762 N — 3456 U — 24477 J
(55×32,+2) (144x8x3) (144x34x5,-3)

(The synodic numbers were already whole, so just increase by a factor of 77).
Now we have Uranus with an exact multiple of Fibonacci numbers: 3,8 and 144.
Neptune and Jupiter are very slightly offset from Fibonacci multiples: N by 2, J by 3.
N = 55 x 8 x 2 x 2, plus 2.
J = 144 x 34 x 5, minus 3.
2,3,5,8,34,55 and 144 are all Fibonacci numbers.
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Other ‘Why Phi?’ posts are listed here.